?gtsv

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 10/15/2026

Version

Public

?gtsv

Computes the solution to the system of linear equations with a tridiagonal coefficient matrix A and multiple right-hand sides.

Syntax

lapack_int LAPACKE_sgtsv(int matrix_layout, lapack_int n, lapack_int nrhs, float *dl,
                         float *d, float *du, float *b, lapack_int ldb);

lapack_int LAPACKE_dgtsv(int matrix_layout, lapack_int n, lapack_int nrhs, double *dl,
                         double *d, double *du, double *b, lapack_int ldb);

lapack_int LAPACKE_cgtsv(int matrix_layout, lapack_int n, lapack_int nrhs,
                         lapack_complex_float *dl, lapack_complex_float *d,
                         lapack_complex_float *du, lapack_complex_float *b,
                         lapack_int ldb);

lapack_int LAPACKE_zgtsv(int matrix_layout, lapack_int n, lapack_int nrhs,
                         lapack_complex_double *dl, lapack_complex_double *d,
                         lapack_complex_double *du, lapack_complex_double *b,
                         lapack_int ldb);

Include Files

mkl.h

Description

The routine solves for X the system of linear equations A*X = B , where A is an n -by- n tridiagonal matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions. The routine uses Gaussian elimination with partial pivoting.

Note that the equation A^T*X = B may be solved by interchanging the order of the arguments du and dl .

Input Parameters

matrix_layout

Specifies whether matrix storage layout is row major ( LAPACK_ROW_MAJOR ) or column major ( LAPACK_COL_MAJOR ).

n

The order of A , the number of rows in B ; n ≥ 0.

nrhs

The number of right-hand sides, the number of columns in B; nrhs≥ 0 .

dl

The array dl (size n - 1) contains the (n - 1) subdiagonal elements of A .

d

The array d (size n ) contains the diagonal elements of A .

du

The array du (size n - 1) contains the (n - 1) superdiagonal elements of A .

b

The array b of size max(1, ldb * nrhs ) for column major layout and max(1, ldb * n ) for row major layout contains the matrix B whose columns are the right-hand sides for the systems of equations.

ldb

The leading dimension of b ; ldb≥ max(1, n)ldb ≥ max(1, n ) for column major layout and ldb ≥ nrhs for row major layout .

Output Parameters

dl

Overwritten by the (n-2) elements of the second superdiagonal of the upper triangular matrix U from the LU factorization of A. These elements are stored in dl(1), ..., dl(n - 2)dl[0], ..., dl[n - 3] .

d

Overwritten by the n diagonal elements of U .

du

Overwritten by the (n-1) elements of the first superdiagonal of U .

b

Overwritten by the solution matrix X .

Return Values

This function returns a value info .

If info = 0 , the execution is successful.
If info = -i , parameter i had an illegal value.

If info = i , U_{i, i} is exactly zero, and the solution has not been computed. The factorization has not been completed unless i = n .

LAPACK 95 Interface Notes

There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.

NOTE:

Matrix Storage Schemes

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?gtsv

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes